A structural model of a micropolar continuum

Abstract In their crystal lattice theory, Born-Von Karman have shown that the long wave approximation to their model yields the equations of the classical theory of elasticity. The Born-Von Karman model assumed that the interaction between the particles can be characterized by a simple spring which allows extensions only. Also, in their model, the dimensions of the particles are shrunk to zero thus resulting in non-orientable mathematical points. In this paper, a two dimensional model composed of orientable points, joined by extensible and flexible rods is presented in order to explain the foundations of the Cosserat [1] or the micropolar continuum [2]. As the long wave approximation from this model, one gets the coupled displacement and microration equations of the micropolar medium, similar to those given by Eringen and Suhubi[2, 3] and by Mindlin[4, 5].